Question

When a cannon shell explodes in mid air

• A. momentum of the system is conserved in all cases.
• B. momentum of the system is conserved only if the shell was moving horizontally.
• C. kinetic energy of the system either remains constant or will decrease.
• D. kinetic energy of the system will always increase

Answer 1

The correct option is A momentum of the system is conserved in all cases.

During explosion, the net force acting on the body is the weight of the system (fragments or particles of the body) which is $mg$, where $m$ is the mass of the body.
In this case, the change in momentum of the system (exploded particles) due to gravitational force (weight $\text{mg})$ is negligible.
$\Rightarrow \Delta P={\int }_0^{\Delta t}{F}_{ext}dt$
$\Rightarrow \Delta P=F_{ext}\Delta t\text{where}{F}_{ext}=mg$

Since $\Delta t\to 0,\Delta P\to 0$

So, the momentum of the system before and after the impact remains the same.

When cannon shell explodes in mid air, it produces some energy in the explosion. We cannot say it will always increase the kinetic energy of the system.
So, option (a) is correct.